Consider the ANOVA table that follows.
 

Analysis of Variance
Source	DF	SS	MS	F
Regression	5	 	4,001.11	 	800.22	 	14.72	 
Residual Error	48	 	2,610.04	 	54.38	 	 	 
Total	53	 	6,611.16	 	 	 	 	 
Standard error of estimate	7.37 About 95% of the residuals will be between what two values? (Round your answers to 2 decimal places.)


To solve this problem, we can use the information provided in the ANOVA table, particularly the standard error of the estimate (which is 7.37). Since about 95% of the residuals are expected to fall within ±1.96 standard deviations (based on the properties of a normal distribution), we will compute the following:

\[
\text{Range of residuals} = \pm 1.96 \times \text{Standard Error of Estimate}
\]

Let's calculate this:

\[
1.96 \times 7.37 = 14.44
\]

Thus, about 95% of the residuals will be between:

\[
\text{Lower bound} = -14.44, \quad \text{Upper bound} = 14.44
\]

So, the residuals will fall between **-14.44** and **14.44**.

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Would you like any further details or have any questions?

Here are 5 related questions you might find interesting:
1. How is the standard error of the estimate calculated in regression analysis?
2. Why do we use 1.96 standard deviations for a 95% confidence interval?
3. What is the relationship between residuals and the accuracy of a regression model?
4. How does an increase in residual variance affect the model's predictions?
5. How would you interpret an ANOVA table with a different F-value?

**Tip:** Always check the assumptions of normality and homoscedasticity when interpreting residuals in regression models.

Consider the ANOVA table that follows.

Analysis of Variance
Source	DF	SS	MS	F
Regression	5	4,001.11	800.22	14.72
Residual Error	48	2,610.04	54.38		
Total	53	6,611.16				
Standard error of estimate	7.37 About 95% of the residuals will be between what two values? (Round your answers to 2 decimal places.)

Explore how to find the 95% confidence interval for residuals based on an ANOVA table in regression analysis. This problem involves using the standard error of estimate and the properties of the normal distribution. Suitable for college-level students.

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